Consider three iid random varaiables from an exponential distribution, $X_1,X_2,X_3 \sim$ Exponential$(1)$, each with a pdf $f(x) = e^{-x} , \space \text{where } x >0$. Determine the conditional pdf of the maximum of the sample given using the minimum of the sample, i.e. $f_{X_{(3)}|X_{(1)}} (y \space|\space x)$.
My process
For a continuous random variable the conditional pdf of a probability function of $X$ given $Y$ is $$f_{X|Y}(x,y) = \dfrac{f(x,y)}{f_Y(y)}$$ From what I can find online, to find the conditional pdf of $Y$ given $X$ we have to find $f_X(x)$, the marginal pdf of $X$ first, which I can do by integrating the joint pdf $f(X_1,X_2,X_3)$. How do I find the joint pdf of these three variables?